In this paper, we consider a delayed stage-structured predator-prey model incorporating prey refuge with Holling type Ⅱ functional response. It is assumed that prey can live in two different regions. One is the prey refuge and the other is the predatory region. Moreover, in real world application, we should consider the stage-structured model. It is assumed that the prey in the predatory region can divided by two stages: Mature predators and immature predators, and the immature predators have no ability to attack prey. Based on Mawhin's coincidence degree and novel estimation techniques for a priori bounds of unknown solutions to Lu = λNu, some sufficient conditions for the existence of periodic solution is obtained. Finally, an example demonstrate the validity of our main results.
Citation: Weijie Lu, Yonghui Xia, Yuzhen Bai. Periodic solution of a stage-structured predator-prey model incorporating prey refuge[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 3160-3174. doi: 10.3934/mbe.2020179
In this paper, we consider a delayed stage-structured predator-prey model incorporating prey refuge with Holling type Ⅱ functional response. It is assumed that prey can live in two different regions. One is the prey refuge and the other is the predatory region. Moreover, in real world application, we should consider the stage-structured model. It is assumed that the prey in the predatory region can divided by two stages: Mature predators and immature predators, and the immature predators have no ability to attack prey. Based on Mawhin's coincidence degree and novel estimation techniques for a priori bounds of unknown solutions to Lu = λNu, some sufficient conditions for the existence of periodic solution is obtained. Finally, an example demonstrate the validity of our main results.
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Weijie Lu, Yonghui Xia, Yuzhen Bai. Periodic solution of a stage-structured predator-prey model incorporating prey refuge[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 3160-3174. doi: 10.3934/mbe.2020179
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